Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain
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Sistemas cuánticos desordenadosKnowledge Area
Física AplicadaSponsors
Fundación Séneca grant 05570/PD/07 and Ministerio de Ciencia e Innovación project number FIS2009-13483-C02-02Publication date
2010-02Publisher
New Journal of PhysicsBibliographic Citation
Clark, S.R., Prior Arce, Javier, Hartmann, M.J., Jaksch, D. y Plenio, M.B. (2010) Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain. New Journal of Physics 12Peer review
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FísicaPhysics
Teoría cuántica
Quantum theory
Abstract
In recent work, Hartmann et al (2009 Phys. Rev. Lett. 102 057202) demonstrated that the classical simulation of the dynamics of open 1D quantum systems with matrix product algorithms can often be dramatically improved by performing time evolution in the Heisenberg picture. For a closed system this was exemplified by an exact matrix product operator (MPO) solution of the time-evolved creation operator of a quadratic fermi chain with a matrix dimension of just two. In this work, we show that this exact solution can be significantly generalized to include the case of an open quadratic fermi chain subjected to master equation evolution with Lindblad operators that are linear in the fermionic operators. Remarkably even in this open system the time evolution of operators continues to be described by MPOs with the same fixed dimension as that required by the solution of a coherent quadratic fermi chain for all times. Through the use of matrix product algorithms the dynamical behaviour of operators ...
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